## Introduction:

The purpose of this experiment is to determine the concentration of nitric acid by titration and monitoring the pH. This is method is also known as an __acid-base titrimetry__ Aliquots of sodium carbonate will be titrated with 0.1N (normality) of nitric acid. From the pH curve, the second equivalence point will be determined as a sharp drop in pH whereby all the sodium carbonate has been consumed and converted to its conjugate acid. The second equivalence point’s nitric acid volume and known weight of sodium carbonate will be used to determine the initial concentration of acid.

## Materials:

pH meter, nitric acid from previous experiment), anhydrous sodium carbonate (ACS grade), buffer solutions (pH 4, 7, and 10), reagent water, three 300mL beakers, large beaker (1 liter), analytical balance, weighing boats, ceramic crucible, dessicator (optional), burette, stand, clamp.

## Procedure:

- Prepare sodium carbonate standard by weighing out approximately 1 gram and baking it in the oven for approximately 30 minutes at 100°C. (This is to remove any water contaminants in the standard, since we want it to be as pure as possible).
- While the Na
_{2}CO_{3}is heating, make 0.1N nitric acid by mixing 1.967 (or approx. 2mL) of HNO_{3 }in 300mL reagent water (slowly add acid to water, never the other way around).

Assuming the nitric acid made from our synthesis is 68 wt%, its normality is found by first calculating molarity:

And because nitric acid only has one proton (H^{+}) , its molarity is equal to normality. In other words, 15.249 M = 15.249 N HNO_{3} - Prepare the burette by rinsing it with a small amount of diluted 0.1N nitric acid solution.
- Fill the burette to 50mL or to the top of the graduated mark. Set this aside for now.
- Prepare the pH meter by calibrating with pH 4, 7 and 10 buffer solutions.
- After the sodium carbonate has been dried, make 3 solutions of it by weighing 0.2 to 0.22 grams, adding each one to a 300 mL beaker and diluting to 75 mL with reagent water. (Record the weights of the sodium carbonate)
- Titrate the standard solutions of sodium carbonate with 0.1N nitric acid while recording the pH (refer to the table under
**Data**for the format).

Start with 2mL increments up to 18 mL of the titrant, then add 1mL incriments until 24mL, then add 2mL increments up to 40 mL, then 1mL increments up to 44mL, then finish off in 2mL increments.

(The purpose of adding 1mL increments is for us to easily observed the equivalence points, which is the sharp drop in pH)

## MSDS:

## Data:

## Calculations:

The math is simple, except we must acknowledge that the sodium carbonate is dibasic, and therefore, reacts with nitric acid in a 1:2 mole ratio.

2HNO_{3} + Na_{2}CO_{3} ⇌ H_{2}CO_{3} + 2NaNO_{2}(**note**: carbonic acid is also found/represented in its dissociated form of carbon dioxide and water)

2HNO_{3} + Na_{2}CO_{3} ⇌ H_{2}O + CO_{2} + 2NaNO_{2}

Also, the acid-base reaction has two equivalence point where the 2^{nd} point is when all the sodium carbonate has been consumed and converted to its conjugate acid. This corresponding volume of nitric acid is plugged into the equation.

First equivalence point: H^{+} + CO_{3}^{2-} ⇌ HCO_{3}^{–}

Results in the first base dissociation constant (k_{b1}): CO_{3}^{2-} + H_{2}O ⇌ HCO_{3}^{–} + OH^{–}

Second equivalence point: H^{+} + HCO_{3}^{–} ⇌ H_{2}CO_{3}

Results in the second base dissociation constant (K_{b2}): HCO_{3}^{–} + H_{2}O ⇌ H_{2}CO_{3} + OH^{–}

The second equivalence point is easily found from looking at the biggest change in pH as nitric acid is added. If the equivalence point is not easily seen from the table, the derivative can be used to determine the largest rate of change within the slope of the titration curve.

At the initial point, only sodium carbonate exists and the solution’s pH is dependent on Na_{2}CO_{3} dissociation, i.e. treat as monoprotic base.

Buffer 1: This is the first buffer region. HNO_{3} (strong acid) is added to Na_{2}CO_{3} (weak base) creates a buffer and is characterized by a shallow slope, mathematically represented by the Henderson-Hasselbach equation, consists of CO_{3}^{2-} and HCO_{3}^{–}

Ve_{1}: This is the first equivalence point and is one of the steepest part of the titration curve consisting of intermediate form HCO_{3}^{–} and mathematically represented by pH = ½(pk_{1} + pk_{2}).

Buffer 2: This is the second buffer region, and is also a shallow region of the curve, mathematically represented by H/H equation, consists of HCO_{3}^{–} and H_{2}CO_{3.}

Ve_{2}: second equivalence point where only the fully protonated form or conjugate acid exists (carbonic acid), mathematically treated as monoprotic acid

Lastly, we also consider the dilution factor when 2mL of nitric acid was diluted to 300mL with reagent water. The entire equation should look like:

This is the concentration (in molars) of nitric acid in 300mL of water. To find the initial concentration of nitric acid:

## Conclusion:

With the standard deviation being a small value of 0.185, the three trials are considered to be close to each other, i.e. not so spread out. Moreover, the relative standard deviation is also small, which means that the data set is clustered around the mean value. These two statistical values indicate high precision or repeatability of the method.

Accuracy is a difficult merit to evaluate because this involves knowing true value from a better method that is outside this user’s capabilities. Knowing the limitations of acid-base titration can help determine its accuracy. This method involves a lot of steps with each having an associated uncertainty and error, such as:

(1) the dilution of nitric acid using a 600mL beaker has ±5% relative uncertainty

(2) pipetting 2mL of HNO_{3} has a very small error contribution

(3) the pH meter has ±0.01 absolute uncertainty from the pH solutions.

In addition to the above uncertainties, the biggest contribution to error is the uncertainty in finding the exact 2^{nd} equivalence point from the addition of nitric acid by drop-wise, and measuring in intervals of 1 mL. However, for a rough estimate of the concentration, determination of nitric acid by acid-base titrimetry is more accurate than volumetric titration. The error in looking for the right indicator color change is more difficult to visually distinguish.

Moreover, the method of creating nitric acid from potassium nitrate and sulfuric acid was performed via distillation with an expected yield of 68% azeotropic nitric acid. Therefore, the average concentration of 15.17M or 67.64% is close to what is expected. Therefore, the method is considered to be both accurate and repeatable with sub-par limits of detection.

## References:

- “Molarity Calculator and Normality Calculator for Acids and Bases.”
*Chemicals – Technical Library*, Millipore Sigma, www.sigmaaldrich.com/chemistry/stockroom-reagents/learning-center/technical-library/molarity-calculator.html. - Harris, Daniel C.
*Exploring Chemical Analysis*. 5th ed., W.H. Freeman and Company, 2013. - My chem 221 lab manual.